Persian mathematician, astronomer and poet best known for the Rubaiyat; also helped reform the solar calendar. Khayyam was an outstanding mathematician and astronomer who wrote several works including Problems of Arithmetic, a book on music and one on algebra before he was 25 years old.
An invitation was sent to Khayyam from shah Malik-Shah in 1073 asking Khayyam to go to Esfahan to set up an Observatory in the city. Other leading astronomers were also brought to the Observatory in Esfahan, and for 18 years Khayyam led the scientists and produced work of outstanding quality. It was a period of peace during which the political situation allowed Khayyam the opportunity to devote himself entirely to his scholarly work.
During this time, Khayyam led work on compiling astronomical tables, and he also contributed to calendar reform; in 1079 Khayyam measured the length of the year as 365.24219858156 days. Khayyam also solved the cubic equation x3 + 200x = 20x2 + 2000 and he found a positive root of this cube by considering the intersection of a rectangular hyperbola and a circle. An approximate numerical solution was then found by interpolation in trigonometric tables. Khayyam seems to have been the first to conceive a general theory of cubic equations, and perhaps even more remarkable was that Khayyam stated that the solution of this equation requires the use of conic sections and not the ruler and compass method, a result which would not be proven for another 750 years!
Khayyam furthered his mathematical talent in his work, the Treatise on Demonstration of Problems of Algebra, which contained a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Another achievement in this text is Khayyam's realisation that a cubic equation can have more than one solution. He demonstrated the existence of equations having two solutions, but unfortunately did not appear to have found that a cubic can have three solutions.
Outside the world of mathematics, Khayyam is best known as a result of Edward Fitzgerald's popular translation in 1859 of nearly 600 short four line poems, the Rubaiyat. Khayyam's fame as a poet has caused some to forget his scientific achievements, which some believe were more substantial than his literary work.
Sources: O'Connor, J J, Robertson, E F. "Omar Khayyam." School of Mathematical and Computational Sciences, University of St. Andrews.; Saudi Aramco World, January-February 2002.